Solve Using the Square Root Property 2x^2+288=0

$2 x^{2} + 288 = 0$

Step 1

Subtract $288$ from both sides of the equation.

$2 x^{2} = - 288$

Step 2

Divide each term in $2 x^{2} = - 288$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 288$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 288}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 288}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 288}{2}$

Simplify the right side.

Divide $- 288$ by $2$ .

$x^{2} = - 144$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 144}$

Step 4

Simplify $\pm \sqrt{- 144}$ .

Rewrite $- 144$ as $- 1 (144)$ .

$x = \pm \sqrt{- 1 (144)}$

Rewrite $\sqrt{- 1 (144)}$ as $\sqrt{- 1} \cdot \sqrt{144}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{144}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{144}$

Rewrite $144$ as $12^{2}$ .

$x = \pm i \cdot \sqrt{12^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm i \cdot 12$

Move $12$ to the left of $i$ .

$x = \pm 12 i$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 12 i$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 12 i$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 12 i, - 12 i$